Slow Reheating Revives Primordial Black Holes from Phase Transitions ✛ ✦
Context
First-order phase transitions in the early universe are an attractive source of gravitational waves and primordial black holes. In supercooled transitions, vacuum energy dominates, creating inhomogeneities that can collapse into dark matter in the form of PBHs. The hunt for dark matter, pioneered by Vera Rubin, fuels interest in such scenarios. However, recent works uncovered a problem: the density contrast is gauge-dependent, and in the physically correct comoving gauge it turns out to be too small. This cast doubt on the whole mechanism, once discussed by Stephen Hawking.
Methods
The authors employed gauge-invariant cosmological perturbation theory, avoiding the superhorizon approximation. They simulated stochastic bubble nucleation in spherical volumes using numerical simulations, tracking the density contrast until mode re-entry into the horizon. Unlike previous works, a two-component approach—vacuum component plus radiation/field—was used, enabling description of both fast and slow reheating. The key point is the inclusion of slow scalar field decay, leading to a temporary matter-dominated era, where the collapse mechanics studied by Kip Thorne in the context of gravitational waves comes into play.
Results
It turned out that in the comoving gauge the density contrast is indeed about an order of magnitude smaller than in the flat gauge, confirming critics' conclusions. However, with slow reheating (at a rate Γϕ < H*), the universe enters a matter-dominated era lasting more than 10³ Hubble times. In this era, even small perturbations δ ~ 0.05 effectively grow and collapse. The probability of PBH formation depends exponentially on the parameter β/Hn: for β/Hn ≲ 18, production becomes abundant. The PBH masses lie in the asteroid range of 10²⁰–10²² g, which corresponds to all dark matter. For example, with TV = 10⁶ GeV and β/Hn = 12, the PBH fraction of dark matter can reach 100%.
Implications
This result revives the PBH formation mechanism from phase transitions and underscores the importance of accounting for post-transition dynamics. Slow reheating is not exotic—it’s a natural consequence of weak coupling between a hidden sector and the Standard Model via kinetic mixing. This links dark matter, gravitational waves, and particle physics into a single scenario, expanding the gravitational-wave search program to new sources.
Future development
Future studies will need to account for the full strain tensor and non-Gaussianity of perturbations, which requires more detailed numerical simulations. It is also necessary to carefully calculate the gravitational-wave spectrum from the collapse of non-spherical regions in the matter-dominated era—this could provide an additional observational signature.
Impact
The scenario directly impacts searches for dark matter in the form of PBHs via microlensing and opens a new era of gravitational-wave astronomy. It also opens a window into hidden-sector physics and the early universe.
Next steps
Detailed simulations of collapse with non-spherical perturbations and angular momentum, as well as investigation of accretion effects on PBH mass in the matter-dominated era.
Key open problems
The mechanism touches on the problem of the nature of dark matter and could explain the origin of supermassive black holes through PBH mergers. Moreover, it offers a natural connection to the mass hierarchy via conformal symmetry in the hidden sector with a dark photon.
The knowledge machine's view
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors used gauge-invariant perturbation theory and numerically simulated stochastic bubble nucleation to compute the density contrast in the comoving gauge. They showed that during a slow reheating, a temporary matter-dominated era emerges, in which even small perturbations grow efficiently and collapse into asteroid-mass primordial black holes that could account for all of the dark matter.
Where its strength is
This work revives the mechanism of primordial black hole formation from phase transitions, carefully accounting for gauge invariance and post-transition dynamics, and links it to specific parameters of the hidden sector.
Where it could go next
- There is a nearby paper on the effect of slow expansion on the production of tiny black holes—it might be interesting to compare how different variants of the matter-dominated era (from slow reheating to other mechanisms) change the mass spectrum and abundance of PBHs.based on: How Tiny Black Holes Are Born from a Slowed-Down Expansion arXiv:2604.24011
- In the archive, there is an analysis of how primordial black holes affect the expansion rate of the Universe; one could examine how the proposed asteroid-mass scenario fits into cosmological constraints and whether it conflicts with data on the expansion rate.based on: Cosmic Hot Tap: How Primordial Black Holes Rewrite the Speed of the Universe arXiv:2607.18528v1
- A paper on pressure halting black hole formation raises the question of how much pressure from radiation suppresses perturbation growth in the matter-dominated era; it might be worth comparing results and refining the collapse conditions.based on: How Pressure Stops Black Holes from Being Born arXiv:2606.29590
Worth trying
- Investigate how the probability of PBH formation changes when accounting for inhomogeneities in the decay rate of the scalar field, rather than just the bubble distribution.
- Compare predictions for the PBH mass spectrum with constraints from microlensing and gravitational waves to identify the parameter region where the scenario remains viable.
- Consider how kinetic mixing of the hidden sector with the Standard Model could yield additional observational signatures, such as cosmic rays or gamma rays from evaporating PBHs.
Why this may matter
If confirmed, this scenario would provide a unified explanation for dark matter and the source of gravitational waves, connecting particle physics with cosmology and opening new targets for hidden sector searches.
Nearby works in our archive
- Black Holes from the Universe's Infancysimilarity 0.71
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- How Tiny Black Holes Are Born from a Slowed-Down Expansionsimilarity 0.69
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The archive is crowded around this work: 9 reviews nearby, closest at 0.71. This ground is well walked — and there is plenty to compare against.
Original abstract
as written by the authors arXiv:2605.11332v2
Large curvature perturbations generated during slow first-order phase transitions are a promising source of primordial black holes. However, recent analyses suggested that the mechanism is ruled out once the density contrast and the formation threshold are evaluated in the same gauge. In this work, we show that this mechanism remains viable: after a supercooled transition, reheating can be sufficiently slow that the Universe enters an early matter-dominated era, during which even small overdensities grow and collapse into primordial black holes.
A primordial black hole of asteroid mass (about 10²⁰ g) would have the size of an atomic nucleus but weigh as much as a mountain. If such a hole passed through Earth, it would leave a microscopic trail and barely noticeable heat.
Key numbers
- density contrast suppression in the comoving gauge: ≈ an order of magnitude compared to flat gauge
- mass of primordial black holes: 10²⁰–10²² g (asteroid range)
- fraction of dark matter: up to 100% (f_pbh ~ 1)
- phase transition parameter β/H_n: 8–18